> Isn't proving a major conjecture enough? Not necessarily. And not because of a lack of tangible rewards, but because of a lack of mathematical ones. Mathema

> Isn't proving a major conjecture enough? Not necessarily. And not because of a lack of tangible rewards, but because of a lack of mathematical ones. Mathematicians are not just after true statements, or proof, but understanding, and new theories that open up new areas of study. For that reason, a new proof of an old theorem is often quite interesting. I seem to recall reading that Wiles' proof of Fermat's last theorem was sensational, but ultimately less exciting than it could be--the proof did not create a new way of viewing or systematizing things so much as apply very specialized machinery to a specific problem. Take that with a grain of salt--I don't have a hundredth of the mathematical background to judge it myself.